Base field \(\Q(\sqrt{11}) \)
Generator \(w\), with minimal polynomial \(x^2 - 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[19,19,-2 w - 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^4 + x^3 - 5 x^2 - x + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 4]$ | $-e^3 - 2 e^2 + 2 e + 3$ |
| 5 | $[5, 5, -w - 4]$ | $\phantom{-}e^3 + e^2 - 3 e$ |
| 7 | $[7, 7, w + 2]$ | $-e^3 - 2 e^2 + 3 e + 2$ |
| 7 | $[7, 7, w - 2]$ | $\phantom{-}e^2 + e - 4$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e^3 + 2 e^2 - 3 e - 5$ |
| 11 | $[11, 11, -w]$ | $-2 e - 3$ |
| 19 | $[19, 19, 2 w - 5]$ | $\phantom{-}e^3 + e^2 - 4 e - 4$ |
| 19 | $[19, 19, -2 w - 5]$ | $\phantom{-}1$ |
| 37 | $[37, 37, 2 w - 9]$ | $-e^3 + 7 e + 2$ |
| 37 | $[37, 37, -2 w - 9]$ | $-4 e^3 - 5 e^2 + 14 e + 2$ |
| 43 | $[43, 43, 2 w - 1]$ | $\phantom{-}e^3 + 3 e^2 - e - 7$ |
| 43 | $[43, 43, -2 w - 1]$ | $\phantom{-}3 e^3 + 3 e^2 - 13 e - 4$ |
| 53 | $[53, 53, -w - 8]$ | $\phantom{-}e^3 - 6 e + 3$ |
| 53 | $[53, 53, w - 8]$ | $-e^3 - 2 e^2 + 5 e$ |
| 79 | $[79, 79, 5 w - 14]$ | $\phantom{-}2 e^3 + 2 e^2 - 10 e - 4$ |
| 79 | $[79, 79, 8 w - 25]$ | $-e^3 + 10 e - 7$ |
| 83 | $[83, 83, -3 w - 4]$ | $-3 e^3 - 2 e^2 + 7 e - 6$ |
| 83 | $[83, 83, 3 w - 4]$ | $-3 e^3 - e^2 + 14 e + 6$ |
| 89 | $[89, 89, -w - 10]$ | $-2 e^2 + 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-2 w - 5]$ | $-1$ |